Authorities were searching Texas' Big Bend area for suspects and witnesses Monday after US Customs and Border Protection agent Rogelio Martinez was allegedly beaten to death with a rock while on patrol.

According to officials, Martinez, 36, and his Big Bend Sector partner were responding to activity near Interstate 10, in the Van Horn Station area on Sunday, when both suffered serious injuries.

Responding agents provided immediate medical care and transported both agents to a local hospital, where Martinez later died from his wounds.

US Customs and Border Protection agent Rogelio Martinez (left and right) lost his life in a suspected rock-throwing ambush on US-Mexico border in Texas

His partner, who has not been named, remains in the local hospital in serious condition.

Martinez had been a border agent since August 2013 and was from El Paso. According to social media posts, he is survived by his fiancee.

Border Patrol spokesmen said they could not provide any details on what caused the agent's injuries or what led to them, but a National Border Patrol Council official told KTSM the assailants were 'undocumented immigrants' who used likely used rocks to beat the agents.

The FBI has taken over the investigation into the fatal incident near the US-Mexico border. An agency official from the El Paso office confirmed that Martinez and his partner 'were not fired upon.'

On Sunday, President Donald Trump seized upon the news of the ambush to push his controversial Mexico wall plans.

Heartbreak: Martinez's fiancee shared this image of the couple on her Facebook page

'Border Patrol Officer killed at Southern Border, another badly hurt. We will seek out and bring to justice those responsible. We will, and must, build the Wall!' Trump said in a tweet.

Texas Governor Greg Abbott and Senator Ted Cruz, a Republican, also publicly commented on the deadly incident that resulted in Martinez's death, characterizing it as an attack.

Cruz said in a statement the nation is grateful 'for the courage and sacrifice of our border agents.'

He also said that what happened on Sunday is a 'stark reminder' that an 'unsecured border' poses a threat to the safety of the communities and border agents tasked with protecting them.

Governor Abbott tweeted in a similar vain: 'Our prayers are with the families of this Border Patrol Agent who was killed & the other who was injured in this attack in Texas,' he wrote. 'Our resources must be increased to prevent these attacks in the future.'

President Donald Trump pushed his Mexico wall plans after one border agent was killed and another injured while on patrol in Texas on Sunday

Authorities said Agent Rogelio Martinez and his Big Bend Sector partner were responding to activity while on patrol near Interstate 10, in the Van Horn Station area when they were both injured. Trump tweeted this statement following the incident

'Our thoughts and prayers are with Agent Martinez and his family, and with the agent who was injured,' officials from the US Customs and Border Protection said in a statement.

Border Patrol records show that Big Bend accounted for about 1 per cent of the more than 61,000 apprehensions its agents made along the Southwest border between October 2016 and May 2017.

The region's mountains and the Rio Grande make it a difficult area for people to cross illegally into the US from Mexico.

The Border Patrol website lists 38 agents who have died since late 2003, some attacked while working along the border, and other fatalities in traffic accidents.